{"id":"https://openalex.org/W2920873618","doi":"https://doi.org/10.1137/17m1113527","title":"Approximation Algorithms for Low-Distortion Embeddings into Low-Dimensional Spaces","display_name":"Approximation Algorithms for Low-Distortion Embeddings into Low-Dimensional Spaces","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2920873618","doi":"https://doi.org/10.1137/17m1113527","mag":"2920873618"},"language":"en","primary_location":{"id":"doi:10.1137/17m1113527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1113527","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.mit.edu/bitstreams/ce25753d-b56c-426e-9593-75ae76c36ec5/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013188587","display_name":"Anastasios Sidiropoulos","orcid":null},"institutions":[{"id":"https://openalex.org/I175669267","display_name":"Carestream (United States)","ror":"https://ror.org/048m16q57","country_code":"US","type":"company","lineage":["https://openalex.org/I175669267"]},{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Anastasios Sidiropoulos","raw_affiliation_strings":["CMU, Pittsburgh, PA 15213","Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607","Edgestream Partners L. P., Princeton, NJ 08540","Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CMU, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"Edgestream Partners L. P., Princeton, NJ 08540","institution_ids":["https://openalex.org/I175669267"]},{"raw_affiliation_string":"Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019980991","display_name":"Mihai B\u00e2doiu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mihai Badoiu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024390954","display_name":"Kedar Dhamdhere","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kedar Dhamdhere","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078381067","display_name":"Anupam Gupta","orcid":"https://orcid.org/0000-0001-5579-3405"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anupam Gupta","raw_affiliation_strings":["MIT, Cambridge, MA 02139"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, MA 02139","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076056716","display_name":"Piotr Indyk","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Piotr Indyk","raw_affiliation_strings":["Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213","Google Inc., Mountain View, CA 94043"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Google Inc., Mountain View, CA 94043","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015933918","display_name":"Yuri Rabinovich","orcid":null},"institutions":[{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Yuri Rabinovich","raw_affiliation_strings":["Department of Computer Science, University of Haifa, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Haifa, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016682913","display_name":"Harald R\u00e4cke","orcid":"https://orcid.org/0000-0001-8797-717X"},"institutions":[{"id":"https://openalex.org/I175669267","display_name":"Carestream (United States)","ror":"https://ror.org/048m16q57","country_code":"US","type":"company","lineage":["https://openalex.org/I175669267"]},{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Harald Racke","raw_affiliation_strings":["CMU, Pittsburgh, PA 15213","Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607","Edgestream Partners L. P., Princeton, NJ 08540","Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CMU, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"Edgestream Partners L. P., Princeton, NJ 08540","institution_ids":["https://openalex.org/I175669267"]},{"raw_affiliation_string":"Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087844619","display_name":"R. Ravi","orcid":"https://orcid.org/0000-0001-7603-1207"},"institutions":[{"id":"https://openalex.org/I175669267","display_name":"Carestream (United States)","ror":"https://ror.org/048m16q57","country_code":"US","type":"company","lineage":["https://openalex.org/I175669267"]},{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"R. Ravi","raw_affiliation_strings":["CMU, Pittsburgh, PA 15213","Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607","Edgestream Partners L. P., Princeton, NJ 08540","Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CMU, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"Edgestream Partners L. P., Princeton, NJ 08540","institution_ids":["https://openalex.org/I175669267"]},{"raw_affiliation_string":"Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1791,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50036775,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"33","issue":"1","first_page":"454","last_page":"473"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.80499267578125},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.7662254571914673},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.691824197769165},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6608019471168518},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5847035646438599},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.581484317779541},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5313794016838074},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.4921974241733551},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.4897949695587158},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4753049314022064},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47034910321235657},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4348057806491852},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3573048710823059},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11560851335525513},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08556929230690002},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.061899274587631226}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.80499267578125},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.7662254571914673},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.691824197769165},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6608019471168518},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5847035646438599},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.581484317779541},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5313794016838074},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.4921974241733551},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.4897949695587158},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4753049314022064},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47034910321235657},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4348057806491852},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3573048710823059},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11560851335525513},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08556929230690002},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.061899274587631226},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1113527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1113527","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/135060","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/135060","pdf_url":"https://dspace.mit.edu/bitstreams/ce25753d-b56c-426e-9593-75ae76c36ec5/download","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM","raw_type":"Article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/34126","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/34126","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Thesis"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/135060","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/135060","pdf_url":"https://dspace.mit.edu/bitstreams/ce25753d-b56c-426e-9593-75ae76c36ec5/download","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM","raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3480834568","display_name":"ITR: Algorithms: From Theory to Application","funder_award_id":"0085982","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4906522373","display_name":"CAREER: Geometric Frontiers in Algorithm Design","funder_award_id":"1453472","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5929981123","display_name":"AF: Small: Approximation Algorithms and Topological Graph Theory","funder_award_id":"1423230","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6484169224","display_name":"ITR/SY+IM+AP: Center for Applied Algorithms","funder_award_id":"0122581","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G97666921","display_name":"New Directions in Approximation Algorithms","funder_award_id":"0430751","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320323220","display_name":"Alexander S. Onassis Public Benefit Foundation","ror":"https://ror.org/017nq0d63"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2920873618.pdf","grobid_xml":"https://content.openalex.org/works/W2920873618.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W934230699","https://openalex.org/W1242194915","https://openalex.org/W1973192023","https://openalex.org/W1995402321","https://openalex.org/W1995848967","https://openalex.org/W2012238497","https://openalex.org/W2014972497","https://openalex.org/W2027697499","https://openalex.org/W2039451540","https://openalex.org/W2054702649","https://openalex.org/W2061451339","https://openalex.org/W2063491776","https://openalex.org/W2074866125","https://openalex.org/W2080608361","https://openalex.org/W2152825437","https://openalex.org/W2157321806","https://openalex.org/W2169371330","https://openalex.org/W2803460775"],"related_works":["https://openalex.org/W4318195686","https://openalex.org/W2081900870","https://openalex.org/W2975999359","https://openalex.org/W4287173569","https://openalex.org/W2796561647","https://openalex.org/W4280497496","https://openalex.org/W4313513739","https://openalex.org/W2009836834","https://openalex.org/W2914691919","https://openalex.org/W1996361334"],"abstract_inverted_index":{"We":[0,51],"present":[1],"several":[2],"approximation":[3,56],"algorithms":[4],"for":[5,28,57],"the":[6,17,29,47,58],"problem":[7,30],"of":[8,31,36,60],"embedding":[9,35],"metric":[10,38],"spaces":[11],"into":[12,16],"a":[13,33,37,41],"line,":[14],"and":[15],"2-dimensional":[18],"plane.":[19],"Among":[20],"other":[21],"results,":[22],"we":[23],"give":[24,52],"an":[25,53],"$O(\\sqrt{n})$-approximation":[26],"algorithm":[27],"finding":[32],"line":[34],"induced":[39,62],"by":[40,63],"given":[42],"unweighted":[43,64],"graph,":[44],"that":[45],"minimizes":[46],"(standard)":[48],"multiplicative":[49],"distortion.":[50],"improved":[54],"$\\tilde{O}(n^{1/3})$":[55],"case":[59],"metrics":[61],"trees.":[65]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-25T07:29:55.448023","created_date":"2025-10-10T00:00:00"}
